Question

23. A two-digit number is four times the sum and three times the product of its digits. Find the number

Answer 1

Hello
Let the digit in the ones place be x and tens place be y
Hence the two digit number = 10y + x
Given that the two digit number = 4 times sum of its digits
⇒ 10y + x = 4(x + y)
⇒ 10y + x = 4x + 4y
⇒ 3x – 6y = 0
⇒ 3x = 6y
∴ x = 2y → (1)
It is also given that the two digit number = 3
times product of its digits
⇒ 10y + x = 3xy
Divide by xy both the sides, we get
10/x +1/y = 3
put x =2y from (1)
5/y + 1/y =3
6/y=3
y=2
Hence, x=4

The two digit number is (10y + x) = 42

Hope it helps

Answer 2

Answer:

24

Step-by-step explanation:

Let the two digit number be 10y+x

it is given that 10y+x=4(x + y)........ (1)

and 10y+x=3xy...(2)

So, 10y+x=4x+4y and  

⇒63y=3x

⇒2y=x

Substituting in (2)

10y+2y=6y^2

⇒12y=6y^2

⇒2=y

⇒x=4

∴ The number is 10×2+4=24

HOPE IT HELPS

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